A longitudinal standing wave y=acoskxcoswt is maintained in a homogeneous medium of density d Find theexpression for space density of

a)potential energy Ep (x,t)

b)kinetic energy Ek (x,t) 

The equation of a standing wave is represented as follows:

Using a trigonometric identity to simplify,

where y₀ is the amplitude of the wave,  is 2 times the frequency (in Hz), k is 2 divided by the wavelength (in meters), and x and t are variables for longitudinal position and time, respectively.

 

Now here given equation is

 

y=acoskx coswt 

 

so velocity  = v = w/k

 

Now find expression for space density